Finding C's time — Time & Work Aptitude Question
Finding C's time: A, B and C together finish a work in 4 days. A alone takes 12 days and B alone 18 days. Answer and worked solution on CodeKairo.
- Topic: Time & Work
- Section: Quantitative Aptitude
- Difficulty: Medium
- Time target: 75 seconds
Question
A, B and C together finish a work in 4 days. A alone takes 12 days and B alone 18 days. How long would C alone take?
Options
- 6 days
- 9 days
- 12 days
- 15 days
Show the answer and the worked solution
Correct answer: B. 9 days
Worked solution
- 1/4 = 9/36, 1/12 = 3/36, 1/18 = 2/36.
- C's rate = 9/36 − 3/36 − 2/36 = 4/36 = 1/9.
- C alone takes 9 days.
Answer: 9 days.
The idea
Put every rate over a common denominator before subtracting. Choosing the LCM of all the times keeps the arithmetic in whole numbers.
Shortcut. Back-substitute: with C = 9, 1/12 + 1/18 + 1/9 = 3/36 + 2/36 + 4/36 = 9/36 = 1/4, exactly the trio's rate.
Common trap. 6 days — subtracting only A's rate (1/4 − 1/12 = 1/6) and forgetting to take B's off as well.